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Is it Brownian or fractional Brownian motion?

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  • Li, Meiyu
  • Gençay, Ramazan
  • Xue, Yi

Abstract

Fractional Brownian motion embeds Brownian motion as a special case and offers more flexible diffusion component for pricing models. We propose test statistics based on bi-power variation for testing Brownian motion against fractional Brownian motion alternatives. To filter out the prevalent existence of finite large jumps, a truncation method based on Hurst index estimator is proposed. Simulation results confirm the consistency of jump truncation framework with desirable empirical size and viable empirical power for our tests.

Suggested Citation

  • Li, Meiyu & Gençay, Ramazan & Xue, Yi, 2016. "Is it Brownian or fractional Brownian motion?," Economics Letters, Elsevier, vol. 145(C), pages 52-55.
    • Handle: RePEc:eee:ecolet:v:145:y:2016:i:c:p:52-55
    DOI: 10.1016/j.econlet.2016.05.012
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    References listed on IDEAS

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    1. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
    2. Barndorff-Nielsen, Ole E. & Graversen, Svend Erik & Jacod, Jean & Shephard, Neil, 2006. "Limit Theorems For Bipower Variation In Financial Econometrics," Econometric Theory, Cambridge University Press, vol. 22(4), pages 677-719, August.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Yacine Aït-Sahalia & Jean Jacod, 2012. "Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data," Journal of Economic Literature, American Economic Association, vol. 50(4), pages 1007-1050, December.
    5. Rostek, Stefan & Schöbel, Rainer, 2006. "Risk preference based option pricing in a fractional Brownian market," Tübinger Diskussionsbeiträge 299, University of Tübingen, School of Business and Economics.
    6. Duan, Yunpeng & Xue, Yi, 2014. "Bipower variation with jumps and correlated returns," Economics Letters, Elsevier, vol. 125(3), pages 367-371.
    7. Myron T. Greene & Bruce D. Fielitz, 1980. "Long-Term Dependence and Least Squares Regression in Investment Analysis," Management Science, INFORMS, vol. 26(10), pages 1031-1038, October.
    8. Lee, Suzanne S. & Hannig, Jan, 2010. "Detecting jumps from Lévy jump diffusion processes," Journal of Financial Economics, Elsevier, vol. 96(2), pages 271-290, May.
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    Cited by:

    1. Jia Yue & Ben-Zhang Yang & Ming-Hui Wang & Nan-Jing Huang, 2019. "Asset Prices with Investor Protection and Past Information," Papers 1911.00281, arXiv.org, revised Apr 2020.
    2. Keshab Shrestha, 2021. "Multifractal Detrended Fluctuation Analysis of Return on Bitcoin," International Review of Finance, International Review of Finance Ltd., vol. 21(1), pages 312-323, March.
    3. Sikora, Grzegorz, 2018. "Statistical test for fractional Brownian motion based on detrending moving average algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 54-62.

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    More about this item

    Keywords

    Fractional Brownian motion; Hurst index test; Bi-power variation; Finite jumps;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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